POZNAN UNIVERSITY OF TECHNOLOGY ACADEMIC JOURNALS No 54 Electrical Engineering 2007 __________________________________________ * Poznan University of Technology. Maciej BARTKOWIAK* Tomasz ŻERNICKI* IMPROVED PARTIAL TRACKING TECHNIQUE FOR SINUSOIDAL MODELING OF SPEECH AND AUDIO The paper presents a simple, yet very effective tracking technique for time-varying sinusoidal partials within sinusoidal and hybrid models of speech and audio. The issues of several existing tracking techniques are discussed in the paper. We extend the classic tracking algorithm of McAulay and Quatieri by the inclusion of frequency and amplitude skew factors estimated in the process of chirp analysis. A simple measure of frequency and amplitude matching is proposed to support reliable pairing of detected quasi-sinusoidal peaks across successive frames. Moreover, the paper proposes an evaluation methodology for quality assessment of tracking algorithms. Keywords: sinusoidal model, partial tracking, chirps, estimation, tracking quality 1. INTRODUCTION Sinusoidal model [1,2], as well as several derived hybrid models [3], are well- established signal analysis transformation and synthesis tools in the field of speech and audio processing. In general, the deterministic part of the signal is modeled as an additive mixture of quasi-sinusoidal components whose parameters are time- varying (1). ∑ ∫ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ τ τ π + ϕ = K k t k k k d f t A t x 1 0 det ) ( 2 cos ) ( ) ( ,. (1) The components are called sinusoidal partials since they locally resemble pure sinusoids. Nevertheless, the underlying amplitude and frequency modulations resulting from the intensity and pitch envelopes of the sound cause the spectral energy of each partial to be spread over certain frequency range. The partial parameters (amplitudes A k (t) and frequencies f k (t)) are estimated from the original signal by the use of time-frequency analysis and tracked in consecutive time instants thus forming the frequency and amplitude trajectories (fig. 1).